For all positive, and for all negative.

This is for row constant and row greater than 0.

And for all negative, we have, also, Hyperbolas, but

this corresponds to rho less than 0.

So from rectangular coordinate lattice, we have obtained this kind of strange

lattice, which covers only these parts of entire space time.

The reason for that is when rho is greater than 0,

it is not hard to see that x1 is greater than models of t.

As a result, for greater than 0, these

coordinates cover only this quadrant of whole entire space time.

And for all less than 0,

these coordinates would cover this quadrant of entire space time.

For the reason that x1 would, in that case, will be less.

Well anyway,

it doesn't matter.

So it is important to stress that all these hyperbolas for

different rho have the same asymptotes, which are just these lines.

And when rho rates become smaller, hyperbole becomes closer to the asymptote.

And as rho goes to zero, hyperbolas degenerate

to the two lines that x one squared is equal to t squared,

which is that x one is equal to plus minus t, which are exactly the same line.

So, these lines are corresponding simultaneously to tau minus infinity,

and the row equals to 0.

Tau plus infinity and row equals to 0, and intermediate values of tau are here.

Intermediate values of row are here.

So we have these kind of strange coordinate systems.

Now, one should notice that this metric does degenerate when rho is 0.

When rho goes to 0, this element of the metric vanishes, and

this is a degeneration of the metric.

This degeneration is very similar to the standard degeneration

of the two-dimensional metric in polar coordinates.

If you have this metric d phi squared.

Obviously, that generates when r goes to zero.

But the generation of the metric doesn't mean that the two dimensional space where

this metric is drawn has any peculiarity at r goes to zero.

The space at r equals zero space itself is completely irregular,

it's just the origin of the space.

Similarly, here, when rho goes to zero, the matrix does degenerate,

but the space-time itself doesn't

have any fixed peculiarity along these like light lines.

This is the same Minkowski flat space that are on these like light lines.

This is just the generation of this method.

And now we're going to discuss the meaning of this degenerating of the metric.

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